Finite Group Databasebeta

C4×#17989452 #34008237

order18688
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#17989452

Splittings

FittingC2×C4×C8×C73 ⋊ C4
SylowC73 ⋊ C4×#336

Subgroups

subgroupG/H
centerC2×C42C2×#64408
commutatorC2×C73C42×C8
FrattiniC22×C4C22×#64408
FittingC2×C4×C8×C73C4
socleC23×C73C2×C42
prime radicalC23×D73C22×C4
cosocleC22×C4×D73C23
hypercenterC2×C4×C8#64408
hypocenterC73C4×#336
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

1312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1091821);